正弦函数图像及余弦函数图像的对称性

Symmetry of Sine and Cosine Function Graphs

利用函数图像关于直线对称的充要条件分析得出:过正弦函数、余弦函数图像上的极值点平行于Y轴的每条直线,都是相应图像的对称轴;同时利用函数图像关于点对称的充要条件分析出:正弦函数、余弦函数图像与X轴的每个交点,都是各自图像的对称中心,从而得出正弦函数图像、余弦函数图像,在定义域区间内既是轴对称图形又是中心对称图形,且相应图像的对称中心和对称轴不是惟一的.

By analyzing the function graphs about the necessary and sufficient conditions of the symmetrical straight lines, this paper concludes that every straight line, which parallels to the Y-axis and crosses the extreme point on sine function or cosine function is the axis of the corresponding graph. Furthermore, by utilizing the function graph about necessary and sufficient conditions of the symmetrical points, this paper indicates that every intersection point of sine function, cosine function and X-axis is the symmetry center of each individual. Therefore, it is concluded that the graphs of sine function and cosine function in the field of definition are both the axial symmetry figure and central symmetry figure, and also the symmetry center and the axis of the corresponding graph are not the only one.